Filter wizard: noise in Sallen Key vs. Multiple Feedback

Question

Hi, 
 I am designing a 2-stage amplifer/filter with a high pass (>10kHz) and low pass (<100kHz) and an overall gain of 1000-2000 (gain ~30-40V/V per stage). My input impedance is approximately 5k (piezo transducer), which limits the smallest resistors a bit for noise reduction. 
 In the Filter Wizard, when comparing the noise simulation figures, it seems that Multiple-feedback topologies have significantly less noise (e.g. a peak of 100nV compared to >1uV for comparable Sallen-Key). By tuning resistor/capacitor values, the noise spectrum can be made quite flat and very low compared to Sallen Key. 
 Is this a real effect, or just an artefact of the simulation? 
 This video: Filtering 101: Sallen-Key vs. Multiple Feedback - YouTube by an Analog Devices engineer says that the noise gain of Multiple Feedback is slightly higher. 
 If the Filter Wizard is right, could someone explain the much lower noise? 
 Independent of this issue, what would be your recommendation for the two stages to minimise noise if I want to limit it to 2 opamps? Would it be better to add a 3rd opamp as an input buffer (accepting additional board space) to interface with the high input impedance, and reduce resistor sizes in the following stages? 
 What is the impact of a virtual ground on noise in your experience? I built the above design with the eval kit using virtual ground, and noticed slightly higher noise when the transducer is referenced to GND (9mV RMS) than referenced to VGND (4.7mV RMS).

Matt.Duff · Accepted Answer

Hi, 
 I'm both the author of the Filter Wizard tool as well as the guy in the video, so I guess I'm the person to answer this one. This is a great question. After looking at the math and running some spice simulations, here's what seems to be the case. (All of the following apply to the lowpass configuration - I did not analyze the high pass configuration.) 
 In the video, I made the comments on the lower noise gain of the Sallen Key based on analysis of the op amp noise gain at lower frequencies. While this is true, it turns out the advantage this gives the Sallen Key in noise is pretty minimal, while the Multiple Feedback configuration has several other noise advantages. It looks like you'll typically get better noise out of the Multiple Feedback configuration, for three reasons: 
 1) The noise gain of the Sallen Key increases as the positive feedback kicks in at the mid-frequencies. This doesn't happen with the Multiple Feedback - in fact its noise gain will go down at higher frequencies. 
 2) The Sallen Key has resistors in line with the noninverting input. Until you get to the higher frequencies, where the noise will get shunted by C2, both the resistor noise of these resistors and the op amp current noise through these resistors gets gained up by the noise gain and contributes to the total noise. The Multiple Feedback configuration typically does not have resistors connected to noninverting input (note: when creating bandpass circuits, these resistors sometimes do exist for higher Q configurations.) 
 3) The Sallen Key has a well known issue of the low pass response turning upward at higher frequencies because the signal feeds forward around the op amp rather than going through it. To mitigate this effect, in the Filter Wizard we tend to use higher value resistors in the Sallen Key than we do in the Multiple Feedback. These larger resistor values create more noise. 
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 If you can afford the board space in your design, I would certainly recommend adding a third stage, both to buffer your sensor, but more importantly, to apply a large amount of gain (say at least 40 dB) in that stage rather than in the filters. By having high gain in the first stage, the noise of the filters won't matter that much. Limiting the gain in the filters will also help your sensitivity to component tolerances. You can also use this same stage to create a simple 1st order filter, so that you bring your total low pass filter up to third order. You can ask the filter wizard for a third order filter to get the component values. 
 
 I don't have any insights on why the virtual ground noise is lower than with a regular ground. 
 Hope this was helpful, 
 Matt)